I’m sure they just gave you the official policy over the phone which is fine. Odds are, if your daughter was late they’d just sigh and send her through (whether it be excused or unexcused, who cares). They aren’t going to want to make a bunch of calls and have a kid sitting in the office half the morning (and a ticked off parent), unless it is a repeated issue. It is likely just a CYA policy to deal with repeat offenders.

I drop my kid off after morning appts and he signs himself in. No parent or note needed

This sounds exactly like my kids’ middle school.

Late and signed in by parent: excused

Late and not signed in by parent: unexcused

If unexcused, it is simply treated as a tardy to 1st period (same as any other tardy). At our school, tardies don’t really mean anything anyway unless they get an absolute ton (which gets them lunch detention)

They won’t just send your kid away if tardy. The worst they would do is call you, and I can’t imagine them bothering to do so for being a few minutes late unless it is a regular occurrence. TBH the front desk at my kids’ school often just gives the kids an excused late pass to first period if only a few minutes late- as long as kid is not a frequent flyer.